JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year HEAT TRANSFER Previous Question Paper (February/March - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
Derive steady state general Heat conduction equation without heat generation in cylindrical systems.
Answer
Consider a small cylindrical element of volume dV = (dr)(r dφ)(dz) in a cylindrical coordinate system (r, φ, z). Applying the energy balance principle for steady-state heat conduction without internal heat generation, the net heat flow into the element must be zero.
The heat conduction rates in the three coordinate directions are given by Fourier's Law:
The net heat flow is the sum of the heat entering minus the heat leaving across the faces of the element:
Substituting the expressions for Q and simplifying by dividing by the volume element (r dr dφ dz), we obtain the general heat conduction equation in cylindrical coordinates:
Write down the equation for conduction of heat through a slab or Plane wall.
Answer
For a plane wall of thickness L, thermal conductivity k, and surface temperatures T1 and T2, the steady-state heat conduction rate Q is given by:
Alternatively, using thermal resistance R_th = L / (k A), the equation is expressed as:
List the assumptions made while analyzing the heat flow from a finned surface.
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A 2cm thick steel slab heated to 525°C is held in air stream having a mean temperature of 25°C. Estimate the time interval when the slab temperature would not depart from the mean value of 25°C by more than 0.5°C at any point in the slab. The steel plate has the following thermo-physical properties: ρ = 7950 kg/m³, cₚ = 455 J/kg°C, k = 46 W/m°C, h (heat transfer coefficient on plate surface) = 36 W/m²°C.
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What are repeating variables and how are they selected for dimensional analysis?
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3000 kg of water is heated per hour from 30°C to 70°C by pumping it through a certain heated section of a 25 mm diameter tube. If the surface of the heated section is maintained at 110°C, estimate length of the heated section and the rate of heat transfer from the tube to water.
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Derive an expression for LMTD for a Parallel Flow Heat Exchangers.
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A hot square plate of 75 cm × 75 cm at 120°C is exposed to atmospheric air at 40°C. Find the heat lost from both surfaces of the plate if it is kept in vertical position.
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Water is boiled at atmospheric pressure by a horizontal polished copper heating element of diameter D = 5 mm and emissivity ε = 0.05 immersed in water. If the surface temperature of the heating wire is 350°C, determine the rate of heat transfer from the wire to the water per unit length of the wire.
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State and explain the Stefan-Boltzmann law of radiation heat transfer, giving the nomenclature involved in it.
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It is required to heat the oil to 300°C for frying purpose. A long ladle is used in frying pan. The section of the ladle is 5 mm × 18 mm. The surrounding air is at 30°C and the thermal conductivity of the ladle material is 205 W/mK. If the temperature at a distance of 380 mm from the oil should not exceed 40°C, determine convective heat transfer coefficient.
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Derive an expression for temperature distribution under steady state in one dimensional heat conduction for a plane wall.
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An electrically heated thin foil of length L = 25 mm and width W = 8 mm is to be used as a wind speed meter. Wind with a temperature T∞ and velocity U∞ blows parallel to the longest side. The foil is internally heated by an electric heater dissipating Q (Watts) from both sides and is to be operated in air with T∞ = 20°C, Cp = 1.005 kJ/kg K, ν = 1.522 × 10⁻⁵ m²/s, ρ = 1.19 kg/m³ and Pr = 0.72. The surface temperature, Ts of the foil is to be measured at the trailing edge - but can be assumed to be constant. Estimate the wind speed when Ts = 32°C and Q = 0.5 W.
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How are heat exchangers classified?
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A double-pipe (shell-and-tube) heat exchanger is constructed of a stainless steel (k = 15.1 W/m°C) inner tube of inner diameter Di = 1.5 cm and outer diameter Do = 1.9 cm and an outer shell of inner diameter 3.2 cm. The convection heat transfer coefficient is given to be hi = 800 W/m²°C on the inner surface of the tube and ho = 1200 W/m²°C on the outer surface. For a fouling factor of Rri = 0.0004 m²°C/W on the tube side and Rro = 0.0001 m²°C/W on the shell side, determine: i) The thermal resistance of the heat exchanger per unit length. ii) The overall heat transfer coefficients, Ui and Uo based on the inner and outer surface areas of the tube, respectively.
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